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Communications in Physics

EIT enhanced self-Kerr nonlinearity in the three-level lambda system under Doppler broadening

Dinh Xuan Khoa, Le Van Doai, Pham Van Trong, Tran Manh Cuong, Vu Ngọc Sau, Nguyen Huy Bang, Le Nguyen Mai Anh

Published Aug 30, 2014• 9 citations
Publisher

Abstract

Using density-matrix theory, an analytical expression of the self-Kerr nonlinear coefficient of a three-level lambda EIT medium for a weak probe light is derived. Influences of the coupling light and Doppler broadening on the self-Kerr coefficient are investigated and compared to experimental observation with a good agreement. The self-Kerr nonlinearity is basically modified and greatly enhanced in the spectral region corresponding to EIT transparent window. Furthermore, sign, slope, and magnitude of the self-Kerr coefficient can be controlled with frequency and intensity of the coupling light and temperature. Such controllable Kerr nonlinearity can find interesting applications in optoelectronic devices working with low-light intensity.

DOI
10.15625/0868-3166/24/3/3915

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EIT enhanced self-Kerr nonlinearity in the three-level lambda system under Doppler broadening

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Using density-matrix theory, an analytical expression of the self-Kerr nonlinear coefficient of a three-level lambda EIT medium for a weak probe light is derived. Influences of the coupling light and Doppler broadening on the self-Kerr coefficient are investigated and compared to experimental observation with a good agreement. The self-Kerr nonlinearity of the medium is modified and greatly enhanced in the spectral region of EIT window. Furthermore, sign, slope, and magnitude of the self-Kerr coefficient can be controlled with frequency and intensity of the coupling light and temperature of the medium. In particular, for a given set of fixed values of the parameter coupling and probe lights, it is possible to choose an optimized temperature with which to obtain the largest magnitude of the self-Kerr coefficient. Such a controllable Kerr nonlinearity can find interesting applications in optoelectronic devices working with low-light intensity at various temperature conditions.

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Journal of the Optical Society of America B•Oct 23, 2019•14 citations
Using density-matrix theory, an analytical expression of the self-Kerr nonlinear coefficient of a three-level lambda EIT medium for a weak probe light is derived. Influences of the coupling light and Doppler broadening on the self-Kerr coefficient are investigated and compared to experimental observation with a good agreement. The self-Kerr nonlinearity is basically modified and greatly enhanced in the spectral region corresponding to EIT transparent window. Furthermore, sign, slope, and magnitude of the self-Kerr coefficient can be controlled with frequency and intensity of the coupling light and temperature. Such controllable Kerr nonlinearity can find interesting applications in optoelectronic devices working with low-light intensity.
Using density-matrix theory, an analytical expression of the self-Kerr nonlinear coefficient of a three-level lambda EIT medium for a weak probe light is derived. Influences of the coupling light and Doppler broadening on the self-Kerr coefficient are investigated and compared to experimental observation with a good agreement. The self-Kerr nonlinearity of the medium is modified and greatly enhanced in the spectral region of EIT window. Furthermore, sign, slope, and magnitude of the self-Kerr coefficient can be controlled with frequency and intensity of the coupling light and temperature of the medium. In particular, for a given set of fixed values of the parameter coupling and probe lights, it is possible to choose an optimized temperature with which to obtain the largest magnitude of the self-Kerr coefficient. Such a controllable Kerr nonlinearity can find interesting applications in optoelectronic devices working with low-light intensity at various temperature conditions.
We propose to use a five-level cascade system to enhance self-Kerr nonlinearity under an electromagnetically induced transparency (EIT) condition. Using density-matrix theory, an expression of the self-Kerr nonlinear coefficient for a weak probe light is derived. Variations of the self-Kerr coefficient with respect to the frequency and intensity of a strong coupling light are investigated. The Kerr nonlinearity is basically modified and enhanced greatly in the spectral regions corresponding to EIT transparent windows. Furthermore, the sign, slope, and magnitude of the self-Kerr coefficient can be controlled with the frequency and intensity of the coupling light. Such a controllable Kerr nonlinearity can find interesting applications in optoelectronic devices working with low light intensity at multiple frequencies.
We study enhancement of self-Kerr nonlinearity in three-level cascade EIT medium by the analytical method. The results apply to the 85Rb atoms and show that, in the presence of the EIT effect, the Kerr nonlinear coefficient is enhanced several order of magnitudes (about 10-5 cm2/W) around transparent region. That is, on the Kerr nonlinear graph the two positive and negative values are found on both sides of the resonant frequency. The amplitude and sign of the Kerr nonlinear coefficient can be controlled versus the intensity or frequency of the coupling laser field. Influence of Doppler broadening leads to a decrease in the amplitude of the Kerr nonlinear coefficient. Analytical results are useful for experimental observation and related applications.
The analytical expression for the self-Kerr nonlinear coefficient in a three-level V-type atomic medium is found in the presence of the Doppler effect. Based on the analytical results, we have analyzed the enhancement and control of the Kerr nonlinear coefficient under the condition of electromagnetically induced transparency. It is shown that the Kerr nonlinear coefficient is significantly enhanced around the resonant frequency of both the probe and coupling fields. Simultaneously, the magnitude and sign of the Kerr nonlinear coefficient are controlled with respect to the intensity and frequency of the coupling laser field. The amplitude of the Kerr nonlinear coefficient decreases remarkably as temperature increases (i.e., the Doppler width increases). The analytical model can find potential applications in photonic devices and can explain experimental observations of the Kerr nonlinear coefficient at different temperatures.
In this work, we study the influence of Doppler broadening on cross-Kerr nonlinearity in a four-level inverted-Y atomic system under electromagnetically induced transparency (EIT) condition. The first- and third-susceptibilities in the presence of Doppler effect are derived as a function of probe, signal and coupling beams and temperature of medium. Under EIT condition, cross-Kerr nonlinearity is enhanced several orders of magnitude compared to that without EIT. The Doppler effect leads to a reduction in the transparent efficiency and thus reduces the amplitude of cross-Kerr nonlinear coefficient. For hot atomic gaseous medium, such consideration of the Doppler effect may be useful for experimental observations and apply to photonic devices operating at different temperature conditions.
In this paper, we propose an analytical model to study the effect of Doppler broadening on self-Kerr nonlinearity in a five-level ladder-type atomic system. First- and third-order susceptibilities and the self-Kerr nonlinear coefficient are found as the function of temperature and parameters of laser fields. The analytical model is applied to hot $^{85}{\rm Rb}$85Rb and $^{87}{\rm Rb}$87Rb atoms, and it is shown that under the electromagnetically induced transparency (EIT) effect, the self-Kerr nonlinear coefficient is enhanced around three transparent spectral regions. When the temperature of atomic vapor increases (i.e., Doppler width increases), the depth and width of the EIT windows decrease accordingly, and therefore the amplitude of the Kerr nonlinear coefficient decreases significantly. In addition, because the frequency gaps between hyperfine levels of upper excited state ${{5\rm D}_{5/2}}$5D5/2 of $^{85}{\rm Rb}$85Rb atoms are much smaller than those of $^{87}{\rm Rb}$87Rb atoms, the EIT windows as well as the nonlinear dispersion curves for $^{85}{\rm Rb}$85Rb atoms are closer than those for $^{87}{\rm Rb}$87Rb atoms as the Doppler effect presents. The analytical results agree well with the experimental observation when reducing to a three-level atomic system. The analytical model can be used to easily fit the experimental observations of self-Kerr nonlinearity in a five-level atomic system under different temperature conditions and apply to a variety of applications relating to all-optical-switching techniques.